Let $R$ be a ring and let $I$ be a proper ideal of $R$.
If $R/I$ has no zero divisors, then is it true that $R$ has no zero divisors?
My attempt: Suppose $R$ has zero divisors, say $ab=0$ for some $a,b\in R^*$. Then $(a+I)(b+I)=ab+I=I$. However, I cannot exclude the case where $a,b\in I$.